Duration
30h Th, 20h Pr
Number of credits
| Bachelor in mathematics | 5 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The aim of this course is to present the Galois theory : fields extensions, normal and algebraic closures, Galois correspondance, solvability of polynomial equations by radicals. The course also contains an application to the rule-and-compas constructible polygons.
Learning outcomes of the learning unit
At the end of the course, the student will be able to present the finite Galois theory, with the historically important application of an example of a polynomial whose roots cannot be calculated by radicals.
Prerequisite knowledge and skills
Good basic knowledge of general algebra (groups, rings, fields and linear algebra).
Planned learning activities and teaching methods
The course will be mainly given with chalk and blackboard. Some illustrations might be given using the Mathematica software.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
Face-to-face learning.
Recommended or required readings
The course will be freely based on the syllabus of G. Hansoul, which is available at the secretariat of the Mathematics Institute. Other references are :
- A. Baker, An introduction to Galois theory.
- I. Stewart, Galois theory, fourth edition, CRC Press (2015).
Exam(s) in session
Any session
- In-person
written exam AND oral exam
Additional information:
One written examination (exerices only) and one oral examination (theory). The assessment methods are identical for both examination periods.
Work placement(s)
Organisational remarks and main changes to the course
This course is organized at the second semester. Information available on eCampus.
Contacts
Emilie Charlier (teacher) - Savinien Kreczman (teaching assistant)
Institute of Mathematics - Bât. B37
Allée de la découverte, 12 - 4000 Liège
Tél. : 04/366.93.84
E-mails : echarlier@uliege.be - savinien.kreczman@uliege.be